Micromechanical modeling of cohesive thermoelastic steady‐state and transient cracking in polycrystalline materials

Abstract

In this paper, a micromechanical formulation is proposed for modeling thermoelastic intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model is based on a multiregion boundary element approach combined with the dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic isotropic behavior, and multiphase aggregates have been considered. Damage evolution along (intergranular or transgranular) interfaces is modeled using thermomechanical cohesive laws, and upon failure, nonlinear frictional contact analysis is introduced to model separation, stick or slip. Steady-state and transient thermoelastic formulations have been modeled, and numerical simulations are presented, not only to demonstrate the validity but also to study the physical implications of the proposed formulation, in comparison with other numerical methods as well as experimental observations and literature results.In polycrystalline materials, the modes of fracture are well recognized and can be categorized as follows: brittle intergranular and transgranular cracking, ductile failure, and, at high temperature, creep has to be taken into account. It is worth noting, however, that Blendell and Coble 3 have measured stress development due to TEA in Al 2 O 3 and showed that the microstructure does not experience any stress relaxation until at very high temperature, close to annealing. Thus, in this work, the effect of creep has not been considered since thermal loading has been applied within the range of temperatures that guarantees no stress relaxation. Moreover, still from the experimental findings in the work of Blendell and Coble, 3 the authors have extrapolated the stress-free temperature, from which it is possible to approximate analytically the maximum local stress due to differential thermal expansion. Results in the present work will be shown in good agreement with these literature results.Experimental methods may be used for such investigations, even though, sometimes, they might be expensive and time consuming due to specific required techniques. Experimental results on grain size dependence and TEA were presented by Rice et al 4 and Rice and Freiman, 5 as well as spontaneous cracking in the work Rice and Pohanka. 6 Experiments and simulations were run by Yousef et al, 7 where residual stresses due to cooling from stress-free status have been investigated. TEA has been studied also in the work of Sridhar et al, 8 where the effect of microcracking due to a local thermal expansion mismatch has a substantial influence on the damage evolution in the polycrystalline aggregate.A popular and powerful approach to investigate such mechanisms is the use of computational micromechanic models. The finite element method (FEM) has been widely used due to the availability of commercial software. Intergranular failure has been studied by modeling grains' interfaces as cohesive surfaces. Two-dimensional (2D) models o...

Thermally-induced fracture analysis of polycrystalline materials by using peridynamics

“…18, for the vertical crack, with the decrease of the amount of the grains, the main crack becomes easier to branch and the crack is more likely to propagate approaching the other edge of the plate. These results agree with the conclusion drawn by Geraci and Aliabadi [17]. The damage plots with the distribution of crystals and the two materials are also provided in Fig.…”

“…In this section a type of ceramic, which is constituted of two materials (silicon carbide and alumina), is considered under thermal loading condition based on an earlier study by Geraci and Aliabadi [17]. They utilize the BZM to investigate the effect of number of grains and material composition (the percentages of the silicon carbide).…”

“…In this study, the PD model is used to analyze the same problem and the effect of the GBC is also taken into consideration. Although the crystal system for silicon carbide and alumina are cubic/hexagonal and trigonal, respectively, according to [17], these two materials can be treated as isotropic materials for simplification. To be able to compare PD results with the results given in [17], same approach is utilized by treating two materials as isotropic materials.…”

“…Although the crystal system for silicon carbide and alumina are cubic/hexagonal and trigonal, respectively, according to [17], these two materials can be treated as isotropic materials for simplification. To be able to compare PD results with the results given in [17], same approach is utilized by treating two materials as isotropic materials. The required parameters for the two materials are collected and summarized in Table 1 The geometry of the model (number of PD points, the patterns of the pre-existing cracks, and the size of the plate) is same as the previous Section 3.…”

“…BEM has been successfully applied to analyze different types of fracture of polycrystalline materials [14,15]. Furthermore, BEM was further extended to model polycrystals to illustrate the crack propagation phenomenon under thermal loading [8,16,17]. Multiscale cohesive zone model (MCZM) was recently developed from CZM by Zeng and Li [18] and it is another useful and improved tool for the simulation of fracture of polycrystalline materials.…”